I have for some time entertained an opinion, in common with some others who have turned their attention tot he subject, that a good series of observations with a Water-Barometer, accurately constructed, might throw some light upon several important points of physical science: amongst others, upon the tides of the atmosphere; the horary oscillations of the counterpoising column; the ascending and descending rate of its greater oscillations; and the tension of vapour at different atmospheric temperatures. I have sought in vain in various scientific works, and in the Transactions of Philosophical Societies, for the record of any such observations, or for a description of an instrument calculated to afford the required information with anything approaching to precision. In the first volume of the History of the French Academy of Sciences, a cursory reference is made, in the following words, to some experiments of M. Mariotte upon the subject, of which no particulars appear to have been preserved. “Le même M. Mariotte fit aussi à l’observatoire des experiences sur le baromètre ordinaire à mercure comparé au baromètre à eau. Dans l’un le mercure s’eléva à 28 polices, et dans Fautre l’eau fut a 31 pieds Cequi donne le rapport du mercure à l’eau de 13½ à 1.” Histoire de I'Acadérmie, tom. i. p. 234. It also appears that Otto Guricke constructed a philosophical toy for the amusement of himself and friends, upon the principle of the water-barometer; but the column of water probably in this, as in all the other instances which I have met with, was raised by the imperfect rarefaction of the air in the tube above it, or by filling with water a metallic tube, of sufficient length, cemented to a glass one at its upper extremity, and fitted with a stop-cock at each end; so that when full the upper one might be closed and the lower opened, when the water would fall till it afforded an equipoise to the pressure of the atmosphere. The imperfections of such an instrument, it is quite clear, would render it totally unfit for the delicate investigations required in the present state of science; as, to render the observations of any value, it is absolutely necessary that the water should be thoroughly purged of air, by boiling, and its insinuation or reabsorption effectually guarded against. I was convinced that the only chance of securing these two necessary ends, was to form the whole length of tube of one piece of glass, and to boil the water in it, as is done with mercury in the common barometer. The practical difficulties which opposed themselves to such a construction long appeared to me insurmountable; but I at length contrived a plan for the purpose, which, having been honoured with the approval of the late Meteorological Committee of this Society, was ordered to be carried into execution by the President and Council.
About one method of calculation in the arbitrary curvilinear basis of the Laplace operator and curl from the vector function
